How to define double shortcut like GG
GG is not actually a keybinding, G starts the grab operator and that reacts on certain keytrokes while it's running modally. It uses a modal map (keymapping) for this ability.

You can edit modal maps in User preferences > Input, but not call arbitrary operators (in fact, only sub-operations defined by the operator in C, like Select or Deselect in Border Select op).

For python-scripted operators, there's an event argument passed to modal() and you can check for keystrokes (event.type, event.value etc.) and react in whatever way.

Detect G keystroke in a modal operator:

import bpy
from bpy.props import IntProperty, FloatProperty


class ModalOperator(bpy.types.Operator):
    """Move an object with the mouse, example"""
    bl_idname = "object.modal_operator"
    bl_label = "Simple Modal Operator"

    first_mouse_x = IntProperty()
    first_value = FloatProperty()

    def modal(self, context, event):
        if event.type == 'MOUSEMOVE':
            delta = self.first_mouse_x - event.mouse_x
            context.object.location.x = self.first_value + delta * 0.01

        elif event.type == 'G':
            self.report({'INFO'}, "G")
            context.object.location.x = self.first_value
            return {'CANCELLED'}

        elif event.type == 'LEFTMOUSE':
            return {'FINISHED'}

        elif event.type in {'RIGHTMOUSE', 'ESC'}:
            context.object.location.x = self.first_value
            return {'CANCELLED'}

        return {'RUNNING_MODAL'}

    def invoke(self, context, event):
        if context.object:
            self.first_mouse_x = event.mouse_x
            self.first_value = context.object.location.x

            context.window_manager.modal_handler_add(self)
            return {'RUNNING_MODAL'}
        else:
            self.report({'WARNING'}, "No active object, could not finish")
            return {'CANCELLED'}


def register():
    bpy.utils.register_class(ModalOperator)


def unregister():
    bpy.utils.unregister_class(ModalOperator)


if __name__ == "__main__":
    register()




Transform Modal Map - what (sub-)operations a possible during the modally running operators: